Question 15:
Sam, a lorry driver, transports x boxes of fruit A and y boxes of fruit B from a farm to a market. The average mass of a box of fruit A is 10 kg and a box of fruit B is 5 kg . The maximum load of the lorry is 70 boxes with the total mass is not more than 500 kg.
(a) Write two inequalities, other than x ≥ 0 and y ≥ 0, which satisfy all the above constraints. [2 marks]
(b) The third constraint is shown on the graph on page 152. The shaded region represents the points which satisfy the constraint.
Write the constraint in words. [1 mark]
(c) On page 152, construct and label the region R which satisfies all the constraints. [2 marks]
(d) Use the graph constructed in (c) to answer the following question:
(i) Nyatakan julat bilangan kotak buah A yang dapat diangkut jika bilangan kotak buah B ialah 20 kotak. State the range of the number of boxes of fruit A that can be transported if the number of boxes of fruit B is 20 boxes.
(ii) The wages for transporting a box of fruit A and a box of fruit B are RM1.50 and RM1.75 respectively. Sam works a maximum of 8 hours per day. A round-trip delivery process takes 3.5 hours.
By drawing the objective function line, find Sam’s maximum total daily wages.
[5 marks]
Answer:
(a) $$ \begin{aligned} & \text { I: } x+y \leqslant 70 \\ & \text { II: } 10 x+5 y \leqslant 500 \\ & 2 x+y \leqslant 100 \end{aligned} $$
(b) y < 3x
The number of boxes of fruit B is less than three times the number of boxes of fruit A.
(c)
(d)(i) 7 < x ≤ 40
(d)(ii) $$ \begin{aligned} & W=1.50 x+1.75 y \\ & W=150 x+175 y \\ & W=6 x+7 y \end{aligned} $$
Let,
6x + 7y = 42
From graph: Maximum (18, 52),
Sam’s maximum total daily wages = RM1.50(18) + RM1.75(52) = RM118
Sam, a lorry driver, transports x boxes of fruit A and y boxes of fruit B from a farm to a market. The average mass of a box of fruit A is 10 kg and a box of fruit B is 5 kg . The maximum load of the lorry is 70 boxes with the total mass is not more than 500 kg.
(a) Write two inequalities, other than x ≥ 0 and y ≥ 0, which satisfy all the above constraints. [2 marks]
(b) The third constraint is shown on the graph on page 152. The shaded region represents the points which satisfy the constraint.
Write the constraint in words. [1 mark]
(c) On page 152, construct and label the region R which satisfies all the constraints. [2 marks]
(d) Use the graph constructed in (c) to answer the following question:
(i) Nyatakan julat bilangan kotak buah A yang dapat diangkut jika bilangan kotak buah B ialah 20 kotak. State the range of the number of boxes of fruit A that can be transported if the number of boxes of fruit B is 20 boxes.
(ii) The wages for transporting a box of fruit A and a box of fruit B are RM1.50 and RM1.75 respectively. Sam works a maximum of 8 hours per day. A round-trip delivery process takes 3.5 hours.
By drawing the objective function line, find Sam’s maximum total daily wages.
[5 marks]
Answer:
(a) $$ \begin{aligned} & \text { I: } x+y \leqslant 70 \\ & \text { II: } 10 x+5 y \leqslant 500 \\ & 2 x+y \leqslant 100 \end{aligned} $$
(b) y < 3x
The number of boxes of fruit B is less than three times the number of boxes of fruit A.
(c)
(d)(i) 7 < x ≤ 40
(d)(ii) $$ \begin{aligned} & W=1.50 x+1.75 y \\ & W=150 x+175 y \\ & W=6 x+7 y \end{aligned} $$
Let,
6x + 7y = 42
From graph: Maximum (18, 52),
Sam’s maximum total daily wages = RM1.50(18) + RM1.75(52) = RM118